The generalized gamma convolutions class of distributions appeared in Thorin's work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the univariate case, the multivariate case and the dependence structures that can arise from it have received little interest in the literature. Furthermore, only one projection procedure for the univariate case was recently constructed, and no estimation procedures are available. By expanding the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimation procedures for both the univariate and multivariate cases. We provide some insights about performance of these procedures, and a convergent series for the density of multivariate gamma convolutions, which is shown to be more stable than Moschopoulos's and Mathai's univariate series. We furthermore discuss some examples.

翻译：在索林的工作中,普遍伽马分流分布类别出现在索林的工作中,同时寻找对数-热和帕雷托分布的无限差异性。虽然这些分布在单体体中已经进行了广泛研究,但从中可能产生的多变情况及其依赖结构对文献没有多大兴趣。此外,最近只为单体体情况建立了一种预测程序,而且没有可用的估计程序。通过将多变性普遍伽马分流的密度扩大为一个带分度的拉格尔基础,我们缩小了差距,并为单体和多变两种情况提供了性能估计程序。我们对这些程序的绩效提供了一些见解,并对多种变形伽马联的密度提供了一系列的趋同,这比莫施普洛斯和马赛的单体变化系列更为稳定。我们进一步讨论了一些例子。